Threaded Theorems

Math embroidery of an SIR model of infectious diseases, with the text "Quite Right SIR". The susceptible curve is purple, the infectious curve is pink, and the recovered curve is green. The embroidery is on yellow fabric in a pink embroidery hoop.

The SIR model describes disease spread by dividing a population into susceptible (S), infectious (I), and recovered (R) groups governed by differential equations. This embroidery shows S decreasing, I rising then falling, and R increasing over time. 🧶 🧮 #MathSky #embroidery #handembroidery

Oops sorry! Forgot alt text for this one. The third image is my binary tree embroidery (tree in the combinatorics/graph sense) - there is a post about it on my profile :)

This embroidery design depicts the region around a saddle point on a 3D surface. A saddle point is a critical point on a surface where the the gradient is zero but instead of being a peak or valley, the surface curves up in one direction and down in another.
🧶 🧮 #MathSky #embroidery #handembroidery

Thanks for sharing!!

I just saw your blog post about doing my aperiodic tiling embroidery pattern! Thank you so much for sharing 💜
#ThreadedTheorems

Excited to be part of the maths art exhibition at Talking Maths in Public at the University of Warwick!! 🧶 🧮 #MathSky #embroidery #handembroidery #TMiP2025 #TMiP25

Math embroidery of aperiodic monotiles - the spectre.

Meet the spectre 👻 the first-ever true aperiodic monotile. For ages, no one knew if a single shape could tile the plane without ever repeating. This tiling uses just one tile, no reflections, has no patterns, and fills space perfectly. 🧶 🧮 #MathSky #embroidery #handembroidery

math embroidery of the Lotka-Volterra model of differential equations to model predator-prey dynamics. Mathematical hand stitching by Threaded Theorems.

This embroidery illustrates the Lotka–Volterra model, showing how predator and prey populations impact each other. The axes show prey 🐰 (x) and predator 🦊 (y) numbers, and each looping orbit represents a repeating cycle of population change over time.
🧶 🧮 #MathSky #embroidery #handembroidery

An embroidery hoop with an embroidery of a full binary tree in green thread with pink french knots at the end of each branch on blue fabric. It evokes a cherry blossom tree. The background is green plants with pink flowers.

🌿✨ This full binary tree branches out over 8 levels, stitched with stem stitch and dotted with French knot leaves. Who knew recursion could look this cute? Template in bio if you want to stitch your own! 🧶 🧮 #MathSky #embroidery

WIP embroidery of a full binary tree, a graph with a root node branching left and right. Each node then has two children or is a leaf (no children). Binary trees are studied in combinatorics, the maths of counting structures. 🧶 🧮 #MathSky #embroidery

The Koch snowflake is a fractal with an infinite perimeter but finite area. Each iteration adds smaller triangles to every edge, making the perimeter grow endlessly while the added area grows very slowly, approaching a limit of about 1.6 times the original triangle’s area.
🧶 🧮 #MathSky #embroidery

This embroidery is of the first published image of the Mandelbrot set, which illustrates how complex numbers behave under an iterative equation. If a complex number stays bounded, it’s part of the set. If it grows, it’s outside the set and coloured, forming the vivid edges.
🧶 🧮 #MathSky #embroidery

This embroidery shows a piece of a Penrose tiling, a pattern made from kites and darts that never repeats. Unlike checkerboards, it's aperiodic. Motifs like this star appear infinitely often, but there’s no way to slide the whole tiling and make it match itself.
🧶 🧮 #MathSky #embroidery

Embroidery in a hoop depicting a Lorenz system

Been thinking a lot about the Lorenz attractor and came across @threadedtheorems.bsky.social’s work and had to give it a shot.

This is incredible!! Took a bit of a break so only just saw this - thanks for sharing!

This embroidery traces the streamlines of slow, sticky flow—what mathematicians call Stokes flow. The closer the lines, the faster the flow. Far away, the sphere’s influence fades, and the lines stretch out to be uniform.
🧶 🧮
#MathSky #embroidery

Close-up of the chaos! These swirling stitches follow the Lorenz system’s rules. Even the tiniest change in starting point decides how many times we loop each lobe. One stitch to the left? Whole new journey 🧶 🧮
#MathSky #embroidery

An embroidery piece of a trajectory of the Lorenz system in orange-red colour gradient thread on light blue fabric. The piece is in an embroidery hoop on dark grey carpet. The design follows a path looping around between two spirals, forming a shape vaguely like butterfly wings. #MathSky #embroidery #mathart #handembroidery #LorenzSystem #mathematics #craft #sewing

The Lorenz system describes how a point’s position in 3D space changes over time. The resulting path forms butterfly-shaped lobes. Small changes in the starting point lead to vastly different trajectories. This is linked to the "butterfly effect" in chaos theory.
#art #MathSky #handembroidery

An image of two embroidery hoops - one with blue fabric and a swirly phase diagram of the Lorenz system, the other with yellow fabric and a design of an aperiodic tiling. Tags: craftsky, embroidery, mathematics, math,

Sneak peak of my newest maths embroidery pieces 🧶 🧮
This is my first time trying to use embroidery transfer paper for my designs, so crossing fingers it works well 🤞
#art #MathSky #handembroidery

math art/ mathematical embroidery of a star from the Penrose tiling in an embroidery hoop. It is a black outline of a star with the kite middle sections filled in with a gradient pink, and the darts in the middle filled in with a baby pink.

WIP maths embroidery.
This star is part of the Penrose tiling, an aperiodic tiling that can cover the plane without having a repeating pattern. In the tiling, small symmetric areas like this star appear an infinite number of times, but they don’t join together in a uniform way.